The current interest in collapse characteristics brought about by crashworthiness requirements ýas shown the need for a better understanding and predictive capability for the thin walled open section structures. In general three possible modes exist in which a loaded thin walled open section column can buckle: 1) they can bend in the plane of one of the principal axes; 2) they can twist about the shear. centre; 3) or they can bend and twist simultaneously. The following study was undertaken to investigate the general failure of thin walled open section structures. A literature survey was conducted and it prevailed that a basic fundamental theoretical study was vital in describing the behaviour of thin walled structural members. The following stages of theoretical study have been completed: 1) Formulation of the stiffness matrix to predict the generalised force-displacement relationships assuming the small displacement theory in the linear elastic range. 2) Formulation of the geometric stiffness matrix to predict the buckling criteria under generalised loading and end constraints in the linear elastic range. 3) Formulation of the compound coordinate transformation matrix to relate local and global displacements or forces. 4) Preparation of the associated finite element computer program to solve general thin walled open sections structural problems.

Macro lambda is a parameter for predicting the weight savings for using different material. Macro lambda approximates the response of a thin-walled structure to a change in material thickness. The relationship between macro lambda and weight savings for material substitution is given. The results of nine major joints for a car cab model are given. Two kinds of structural element for weight advantage of aluminum, magnesium and other light materials are given: curved beam in-plane bending, curved beam out-of-plane bending. Bulkhead reinforcement is given for a T-Joint model. The application shows a dramatic reduction of macro lambda for T-Joint x moment and y moment load, which means the weight advantage of light materials is reduced after the reinforcement applied. For the z moment load T-Joint model, adding center layer reinforcement gives the largest reduction of macro lambda and maximum von Mises stress. The bulkhead reinforcement is then used for two car cab joints: B-pillar to rocker joint and hinge pillar to rocker joint. The results indicate that the bulkhead reinforcement near the center area gives the biggest reduction for macro lambda. Micro lambda, which is a value for element level, is introduced. The relationship between micro lambda and force distribution is given. Then it is used for the analysis of the force distribution along curved beam model when the thickness of the model is doubled. The results indicate that the force is redistributed from the corner to center of the flange for the curved beam model. So for curved beam model, light material such as aluminum, magnesium, which is thicker, is more efficiently used than steel. Micro lambda is used for the analysis of B-pillar to rocker joint of a car cab. The result indicates that the maximum micro lambda area is just the area where we apply the optimum bulkhead reinforcement. Micro lambda is also used for the analysis of AISI PNGV bending model. The result shows that the C-pillar area is the major problem area. Several reinforcements for the C-pillar area are given. The result shows that layer 31172 is most important for increasing the stiffness.

In this thesis, we have developed a Subtructured Finite Element / eXtended Finite Element (S-FE/XFE) method. The S-FE/XFE method consists in decomposing the geometry into safe FE-domains and cracked XFE-domains, and solving the interface problem with the Finite Element Tearing and Interconnecting method (FETI).This method allows for handling complex crack configurations in 3D structures with common commercial FE software that do not feature the XFEM. The method is also extended to a mixed dimensional formulation, where the FE-domain is discretised with shell elements while the XFE-domain is modelled with three-dimensional solid elements. This is the so-called S-FE Shell/XFE 3D method. The mixed dimensional formulation is more convenient than a full XFE-3D formulation because it significantly reduces the computational cost and it is more accurate compared to a full shell model because it includes three-dimensional local features such as three-dimensional crack. The compatibility of the displacements through the interface is ensured using the Reissner-Mindlin equation. The method has been extensively validated towards both academic problems and semi-industrial benchmarks in order to demonstrate the benefits of this approach. Among them, the S-FE/XFE method is applied to a crack analysis in a section of a compressor drum of a turbofan engine. The results obtained with the S-FE/XFE method are compared with those obtained with a standard FE computation. Furthermore, two applications of the S-FE shell/XFE 3D approach are proposed. First the load carrying capacity of a section of stiffened panel containing a through-the-thickness crack is investigated (this is the one-bay crack configuration). Second, the ability of the method for handling small surface cracks in large finite element models is addressed by looking at a generic 'large pressure panel' presenting realistic crack configurations.

In design of an aircraft structure, the great emphasis is placed on achieving high weight efficiency. This thesis is focused on the stress analysis of the spars with thin web with or without web openings, which is one of the most important parts of the airplane structures. In comparison with traditional spars or beams, which are widely used in civil engineering applications, the design of the beam with thin web is more complicated. Thesis contains useful information for analytical calculation of this type of spars and its verification using finite element method and experimental measurement.

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